Number System Class 9 MCQ Online Test

1. Under-root 225 is Rational.

True

False

A rational number is defined as any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. The square root of 225 is 15, which can be expressed as the fraction 15/1. Since 15/1 is a quotient of two integers, the square root of 225 is rational. Therefore, the statement "Under-root 225 is Rational" is true.

Explanation

A rational number is defined as any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. The square root of 225 is 15, which can be expressed as the fraction 15/1. Since 15/1 is a quotient of two integers, the square root of 225 is rational. Therefore, the statement "Under-root 225 is Rational" is true.

2. The decimal expansion of 1.01001000100001000001..... is?

Non-Terminating

Non Repeating

Non Terminating but Repeating

Non-Terminating Non Repeating

The given decimal expansion is non-terminating because it continues indefinitely without reaching an end. It is also non-repeating because there is no pattern that repeats in the digits of the decimal. Therefore, the correct answer is "Non-Terminating Non Repeating".

Explanation

The given decimal expansion is non-terminating because it continues indefinitely without reaching an end. It is also non-repeating because there is no pattern that repeats in the digits of the decimal. Therefore, the correct answer is "Non-Terminating Non Repeating".

3. Rational Number can never have Non-Terminating Non-Repeating Decimal Expansion.

True

False

Rational numbers can never have a non-terminating, non-repeating decimal expansion because all rational numbers can be expressed as a fraction of two integers. When a rational number is expressed as a decimal, it either terminates (ends) or repeats a pattern. This is because the decimal representation of a rational number is determined by the numerator and denominator of the fraction. If the decimal does not terminate or repeat, it means that the fraction cannot be expressed as a ratio of two integers, making it an irrational number. Therefore, the statement is true.

Explanation

Rational numbers can never have a non-terminating, non-repeating decimal expansion because all rational numbers can be expressed as a fraction of two integers. When a rational number is expressed as a decimal, it either terminates (ends) or repeats a pattern. This is because the decimal representation of a rational number is determined by the numerator and denominator of the fraction. If the decimal does not terminate or repeat, it means that the fraction cannot be expressed as a ratio of two integers, making it an irrational number. Therefore, the statement is true.

4. The decimal representation of a Rational Number cannot be:

Terminating

Non- Terminating

Non Terminating but Repeating

Non-Terminating Non Repeating

Decimal Expansions of a Rational Number can be either Terminating or Non-Terminating but Repeating.

Explanation

Decimal Expansions of a Rational Number can be either Terminating or Non-Terminating but Repeating.

5. The square of an irrational number is always rational? Is the state true or false?

True

False

The statement "The square of an irrational number is always rational" is false. This is because when an irrational number is squared, the result can be either rational or irrational. For example, the square of the irrational number √2 is 2, which is rational. However, the square of the irrational number √3 is 3, which is also irrational. Therefore, the statement is not always true, making the correct answer false.

Explanation

The statement "The square of an irrational number is always rational" is false. This is because when an irrational number is squared, the result can be either rational or irrational. For example, the square of the irrational number √2 is 2, which is rational. However, the square of the irrational number √3 is 3, which is also irrational. Therefore, the statement is not always true, making the correct answer false.

6. Every Whole Number is not a:

Real Number

Natural Number

Integer

Rational Number

A natural number is a positive whole number that is used for counting and ordering. However, not every whole number is a natural number because natural numbers do not include zero. Therefore, the statement "Every Whole Number is not a Natural Number" is correct.

Explanation

A natural number is a positive whole number that is used for counting and ordering. However, not every whole number is a natural number because natural numbers do not include zero. Therefore, the statement "Every Whole Number is not a Natural Number" is correct.

7. The number of Rational Numbers between 15 and 18 is finite.

True

False

The statement is false because there are infinitely many rational numbers between any two given numbers. In this case, between 15 and 18, we can find an infinite number of rational numbers such as 15.1, 15.01, 15.001, and so on. Therefore, the number of rational numbers between 15 and 18 is not finite.

Explanation

The statement is false because there are infinitely many rational numbers between any two given numbers. In this case, between 15 and 18, we can find an infinite number of rational numbers such as 15.1, 15.01, 15.001, and so on. Therefore, the number of rational numbers between 15 and 18 is not finite.

8. Under-root 0.4 is Rational.

True

False

The statement "Under-root 0.4 is Rational" is false. A rational number is defined as a number that can be expressed as the ratio of two integers, where the denominator is not zero. The square root of 0.4 is an irrational number because it cannot be expressed as a fraction of two integers. Therefore, the correct answer is false.

Explanation

The statement "Under-root 0.4 is Rational" is false. A rational number is defined as a number that can be expressed as the ratio of two integers, where the denominator is not zero. The square root of 0.4 is an irrational number because it cannot be expressed as a fraction of two integers. Therefore, the correct answer is false.

9. The value of 1.999... in the Vulgar Fraction is:

19/10

199999/100000

2

1/9

The value of 1.999... in the Vulgar Fraction is 2. This is because the decimal 1.999... represents an infinite repeating pattern of 9s after the decimal point. When this pattern is converted to a fraction, it can be simplified to 2/1, which is equal to 2.

Explanation

The value of 1.999... in the Vulgar Fraction is 2. This is because the decimal 1.999... represents an infinite repeating pattern of 9s after the decimal point. When this pattern is converted to a fraction, it can be simplified to 2/1, which is equal to 2.

10. The Maximum Number of digits in the Repeating block of digits in the decimal expansion of 3/13 is _______?

The maximum number of digits in the repeating block of digits in the decimal expansion of 3/13 is 6. This can be determined by performing the long division of 3 by 13. After the decimal point, the digit 2 is repeated, resulting in a repeating block of 6 digits.

Explanation

The maximum number of digits in the repeating block of digits in the decimal expansion of 3/13 is 6. This can be determined by performing the long division of 3 by 13. After the decimal point, the digit 2 is repeated, resulting in a repeating block of 6 digits.

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